A time-variant analysis of the 1/f/sup 2/ phase noise in CMOS parallel LC-tank quadrature oscillators

Abstract

Abstract-This paper presents a study of 1 2 phase noise in quadrature oscillators built by connecting two differential LC-tank oscillators in a parallel fashion. The analysis clearly demonstrates the necessity of adopting a time-variant theory of phase noise, where a more simplistic, time-invariant approach fails to explain numerical simulation results even at the qualitative level. Two topologies of 5-GHz parallel quadrature oscillators are considered, and compact but nevertheless highly general, closed-form formulas are derived for the phase noise caused by the losses in the LC-tanks and by the noisy currents in the MOS transistors. A large number of spectreRF simulations, covering a wide range of working conditions for the oscillators, is used to validate the theoretical analysis.

Comparative study of gigahertz CMOS LC quadrature voltage-controlled oscillators with relevance to phase noise

“…The theory presented in [25] can be easily applied to LC coupled oscillators and closed form analysis can be made. Other linear models and comprehensive analysis of cross-coupled VCOs are presented in [26][27][28][29]. A similar model to those presented in these papers, is shown in Fig.…”

Analysis and Design of a Double-Quadrature CMOS VCO for Subharmonic Mixing at $Ka$-Band

“…From the theory of quadrature oscillators, it is well known that, for a fixed current consumption, increasing oscillators coupling deteriorates the phase-noise performance [22]- [25]. The recent work by Romano et al [17] extends the theory developed by the same authors for the quadrature case [23] to an arbitrary number of phases.…”

“…Applying the analytical technique proposed in [25], the following expression of the tank ISF for the case of coupled oscillators can be derived: 1 (9) with where the angle is used instead of for simplicity, is the number of phases (including differential ones), and is the angle between the two oscillator phases driving the same tank. Notice that, through , magnitude and phase of depend on and .…”

“…It is worth remarking that the phase noise generated by , being stationary, can also be found via an alternative LTI analysis, as shown in [17], while the correct evaluation of the phase noise contributed by all transistors necessitates a truly LTV approach since there the phase of the ISF plays a key role. 1 The actual calculations follow the procedure found in [25,Appendix]. They are omitted here for space consideration.…”

A low power, low phase noise, square wave LC quadrature VCO and its comprehensive analysis for ISM band

“…In fact, the best curve fit for the data has a 47.5 phase shift from quadrature. A good approximation of phase deviation from ideal quadrature undergone by the ISF is [13]:…”